Multipolar Phases Research Articles

Cascade of magnetic-field-driven quantum phase transitions in Ce3Pd20Si6

Magnetically hidden order is a hypernym for electronic ordering phenomena that are visible to macroscopic thermodynamic probes but whose microscopic symmetry cannot be revealed with conventional neutron or x-ray diffraction. In a handful of f-electron systems, the ordering of odd-rank multipoles leads to order parameters with a vanishing neutron cross-section. Among them, Ce$_3$Pd$_{20}$Si$_6$ is known for its unique phase diagram exhibiting two distinct multipolar-ordered ground states (phases II and II'), separated by a field-driven quantum phase transition associated with a putative change in the ordered quadrupolar moment from $O_2^0$ to $O_{xy}$. Using torque magnetometry at subkelvin temperatures, here we find another phase transition at higher fields above 12 T, which appears only for low-symmetry magnetic field directions $\mathbf{B} \parallel \langle11L\rangle$ with $1 < L \leq 2$. While the order parameter of this new phase II'' remains unknown, the discovery renders Ce$_3$Pd$_{20}$Si$_6$ a unique material with two field-driven phase transitions between distinct multipolar phases. They are both clearly manifested in the magnetic-field dependence of the field-induced (111) Bragg intensities measured with neutron scattering for $\mathbf{B} \parallel [112]$. We also find from inelastic neutron scattering that the number of nondegenerate collective excitations induced by the magnetic field correlates with the number of phases in the magnetic phase diagram for the same field direction. Furthermore, the magnetic excitation spectrum suggests that the new phase II'' may have a different propagation vector, revealed by the minimum in the dispersion that may represent the Goldstone mode of this hidden-order phase.

How Correlations and Spin-Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels.

Spin-orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d1 transition-metal compounds. The latter effect has been studied since the 1960s on t2g1 octahedral ML6 units in both molecular complexes and extended solid-state lattices. Here we analyze the Jeff = 3/2 quartet ground state of larger cubane-like M4L4 entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin-orbit coupling acts on molecular-like, delocalized t2 orbitals. Using quantum chemical methods, we pin down the interplay of spin-orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t21. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

Field-Angle-Resolved Magnetic Excitations as a Probe of Hidden-Order Symmetry in CeB6

In contrast to magnetic order formed by electrons’ dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as “hidden order.” Previously, the hidden order in phase II was identified as primary antiferroquadrupolar and field-induced octupolar order. Here, we present a combined experimental and theoretical investigation of collective excitations in phase II of CeB6. Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the low-energy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in a rotating field is calculated within a localized approach using the pseudospin representation for the Γ8 states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at a constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of intermultipolar interactions that stabilize hidden-order phases.6 MoreReceived 6 January 2020Revised 20 February 2020Accepted 5 March 2020DOI:https://doi.org/10.1103/PhysRevX.10.021010Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsHeavy-fermion systemsStrongly correlated systemsTechniquesInelastic neutron scatteringCondensed Matter, Materials & Applied Physics

A quantum liquid of magnetic octupoles on the pyrochlore lattice.

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles1. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in-2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice2–4 in rare-earth pyrochlores. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders5–6. Here we show that the correlated ground state of a Ce3+-based pyrochlore, Ce2Sn2O7, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus-2-minus’ rule7–8. Our work identifies Ce2Sn2O7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.

We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.

Interplay of interchain interactions and exchange anisotropy: Stability and fragility of multipolar states in spin-12quasi-one-dimensional frustrated helimagnets

We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-$\frac{1}{2}$ chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.

Degeneracies and exotic phases in an isotropic frustrated spin-1/2 chain

In the presence of an axial magnetic field, a frustrated isotropic J1–J2 model system shows many exotic phases, such as vector chiral and multipolar phases. In this paper, the phase boundaries of these exotic phases are calculated based on the order parameters, energy level crossings and magnetization jumps in the system. The order parameter of the vector chiral phase is calculated using the broken symmetry states at a finite magnetic field. The exact diagonalization and the density matrix renormalization group results are used to show that the vector chiral phase exists only in a narrow range of J2/J1 parameter space. In the quadrupolar phase, the magnetization jumps can be associated with the binding energy of two magnons localized at two different legs of the zigzag chain. The energy level crossings and degeneracies in the presence of the axial magnetic field are studied in detail using the exact diagonalization method.

Cytogenetic studies of chromium (III) oxide nanoparticles on Allium cepa root tip cells

The current study evaluates the cytogenetic effects of chromium (III) oxide nanoparticles on the root cells of Allium cepa. The root tip cells of A. cepa were treated with the aqueous dispersions of Cr2O3 nanoparticles (NPs) at five different concentrations (0.01, 0.1, 1, 10, and 100μg/mL) for 4hr. The colloidal stability of the nanoparticle suspensions during the exposure period were ascertained by particle size analyses. After 4hr exposure to Cr2O3 NPs, a significant decrease in mitotic index (MI) from 35.56% (Control) to 35.26% (0.01μg/mL), 34.64% (0.1μg/mL), 32.73% (1μg/mL), 29.6% (10μg/mL) and 20.92% (100μg/mL) was noted. The optical, fluorescence and confocal laser scanning microscopic analyses demonstrated specific chromosomal aberrations such as—chromosome stickiness, chromosome breaks, laggard chromosome, clumped chromosome, multipolar phases, nuclear notch, and nuclear bud at different exposure concentrations. The concentration-dependent internalization/bio-uptake of Cr2O3 NPs may have contributed to the enhanced production of anti oxidant enzyme, superoxide dismutase to counteract the oxidative stress, which in turn resulted in observed chromosomal aberrations and cytogenetic effects. These results suggest that A. cepa root tip assay can be successfully applied for evaluating environmental risk of Cr2O3 NPs over a wide range of concentrations.

Parity-Breaking Phases of Spin-Orbit-Coupled Metals with Gyrotropic, Ferroelectric, and Multipolar Orders.

We study Fermi liquid instabilities in spin-orbit-coupled metals with inversion symmetry. By introducing a canonical basis for the doubly degenerate Bloch bands in momentum space, we derive the general form of Landau interaction functions. A variety of time-reversal-invariant, parity-breaking phases is found, whose Fermi surface is spontaneously deformed and spin split. In terms of symmetry, these phases possess gyrotropic, ferroelectric, and multipolar orders. The ferroelectric and multipolar phases are accompanied by structural distortions, from which the electronic orders can be identified. The gyrotropic phase exhibits a unique nonlinear optical property. We identify correlated electron materials that exhibit these parity-breaking phases, including LiOsO(3) and Cd(2)Re(2)O(7).

Helical multiferroics for electric field controlled quantum information processing

Magnetoelectric coupling in helical multiferroics allows us to steer spin order with electric fields. Here we show theoretically that in a helical multiferroic chain quantum information processing as well as quantum phases are highly sensitive to electric ($E$) field. Applying $E$ field, the quantum state transfer fidelity can be increased and made directionally dependent. We also show that $E$ field transforms the spin-density-wave/nematic or multipolar phases of a frustrated ferromagnetic spin$\text{\ensuremath{-}}\frac{1}{2}$ chain in chiral phase with a strong magnetoelectric coupling. We find sharp reorganization of the entanglement spectrum as well as a large enhancement of fidelity susceptibility at Ising quantum phase transition from nematic to chiral states driven by electric field. These findings point to a tool for quantum information with low power consumption.

Prdm8 Regulates the Morphological Transition at Multipolar Phase during Neocortical Development

Here, we found that the PR domain protein Prdm8 serves as a key regulator of the length of the multipolar phase by controlling the timing of morphological transition. We used a mouse line with expression of Prdm8-mVenus reporter and found that Prdm8 is predominantly expressed in the middle and upper intermediate zone during both the late and terminal multipolar phases. Prdm8 expression was almost coincident with Unc5D expression, a marker for the late multipolar phase, although the expression of Unc5D was found to be gradually down-regulated to the point at which mVenus expression was gradually up-regulated. This expression pattern suggests the possible involvement of Prdm8 in the control of the late and terminal multipolar phases, which controls the timing for morphological transition. To test this hypothesis, we performed gain- and loss-of-function analysis of neocortical development by using in utero electroporation. We found that the knockdown of Prdm8 results in premature change from multipolar to bipolar morphology, whereas the overexpression of Prdm8 maintained the multipolar morphology. Additionally, the postnatal analysis showed that the Prdm8 knockdown stimulated the number of early born neurons, and differentiated neurons located more deeply in the neocortex, however, majority of those cells could not acquire molecular features consistent with laminar location. Furthermore, we found the candidate genes that were predominantly utilized in both the late and terminal multipolar phases, and these candidate genes included those encoding for guidance molecules. In addition, we also found that the expression level of these guidance molecules was inhibited by the introduction of the Prdm8 expression vector. These results indicate that the Prdm8-mediated regulation of morphological changes that normally occur during the late and terminal multipolar phases plays an important role in neocortical development.

Magnetic phase diagrams of classical triangular and kagome antiferromagnets

We investigate the effect of geometrical frustration on theH–T phase diagrams of the classical Heisenberg antiferromagnets on triangular and kagomelattices. The phase diagrams for the two models are obtained from large-scale Monte Carlosimulations. For the kagome antiferromagnet, thermal fluctuations are unable to liftdegeneracy completely and stabilize translationally disordered multipolar phases. We find asubstantial difference in the temperature scales of the order by disorder effect related todifferent degeneracy of the low- and the high-field classical ground states in thekagome antiferromagnet. In the low-field regime, the Kosterlitz–Thouless transitioninto a spin-nematic phase is produced by unbinding of half-quantum vortices.

Thermodynamics of multiferroic spin chains

The minimal model to describe many spin chain materials with ferroelectric properties is the Heisenberg model with ferromagnetic nearest neighbor coupling J1 and antiferromagnetic next-nearest neighbor coupling J2. Here we study the thermodynamics of this model using a density-matrix algorithm applied to transfer matrices. We find that the incommensurate spin-spin correlations - crucial for the ferroelectric properties and the analogue of the classical spiral pitch angle - depend not only on the ratio J2/|J1| but also strongly on temperature. We study small easy-plane anisotropies which can stabilize a vector chiral order as well as the finite-temperature signatures of multipolar phases, stable at finite magnetic field. Furthermore, we fit the susceptibilities of LiCuVO4, LiCu2O2, and Li2ZrCuO4. Contrary to the literature, we find that for LiCuVO4 the best fit is obtained with J2 ~ 90 K and J2/|J1| ~ 0.5 and show that these values are consistent with the observed spin incommensurability. Finally, we discuss our findings concerning the incommensurate spin-spin correlations and multipolar orders in relation to future experiments on these compounds.

The frustrated ferromagnetic S = 1/2 Heisenberg chain in a magnetic field – How multipolar spin correlations emerge from magnetically ordered states

We present the phase diagram of the frustrated ferromagnetic S = 1/2 Heisenberg J1-J2 chain in a magnetic field, obtained by large scale exact diagonalizations and densitymatrix-renormalization-group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin multipolar Luttinger liquid phases up to hexadecupolar order are found. Starting from classical considerations, we point out that various multipolar correlations are imprinted in a magnetic state and that they can survive the onset of frustration and quantum fluctuations which destroy the conventional magnetic order. Our results also shed new light on previously discovered spin multipolar phases in two-dimensional S = 1/2 quantum magnets in a magnetic field.

Vector chiral and multipolar orders in the spin-12frustrated ferromagnetic chain in magnetic field

We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor ${J}_{1}$ and antiferromagnetic next-nearest-neighbor ${J}_{2}$ exchange couplings in the presence of magnetic field. We use both numerical approaches (the density-matrix renormalization-group method and exact diagonalization) and effective-field-theory approach and obtain the ground-state phase diagram for wide parameter range of the coupling ratio ${J}_{1}/{J}_{2}$. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferronematic spin correlation and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic $(p=3)$ and quartic $(p=4)$ phases, are formed through binding of $p$ magnons near the saturation fields, showing quasi-LRO of antiferromultipolar spin correlations. The multipolar phases cross over to spin-density-wave phases as the magnetic field is decreased before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., ${\text{LiCuVO}}_{4}$) are discussed.